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Differential equations
Introduction to Differential equations
THEORY
T
1.
The notion of differential equation
PRACTICE
P
2.
The notion of differential equation
6
THEORY
T
3.
Notation for ODEs
PRACTICE
P
4.
Notation for ODEs
4
THEORY
T
5.
Order and degree of an ODE
PRACTICE
P
6.
Order and degree of an ODE
4
THEORY
T
7.
Solutions of differential equations
PRACTICE
P
8.
Solutions of differential equations
6
THEORY
T
9.
Linear ODEs
PRACTICE
P
10.
Linear ODEs
7
Direction field
THEORY
T
1.
Direction fields
PRACTICE
P
2.
Direction fields
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THEORY
T
3.
Euler's method
PRACTICE
P
4.
Euler's method
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THEORY
T
5.
Autonomous ODEs
PRACTICE
P
6.
Autonomous ODEs
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THEORY
T
7.
Existence and uniqueness of solutions of ODEs
PRACTICE
P
8.
Existence and uniqueness of solutions of ODEs
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THEORY
T
9.
Solution strategy on the basis of the slope field
PRACTICE
P
10.
Solution strategy on the basis of the slope field
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Separation of variables
THEORY
T
1.
Differentials
PRACTICE
P
2.
Differentials
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THEORY
T
3.
Differential forms and separated variables
PRACTICE
P
4.
Differential forms and separated variables
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THEORY
T
5.
Solving ODEs by separation of variables
PRACTICE
P
6.
Solving ODEs by separation of variables
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Linear first-order differential equations
THEORY
T
1.
Uniqueness of solutions of linear first-order ODEs
PRACTICE
P
2.
Uniqueness of solutions of linear first-order ODEs
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THEORY
T
3.
Linear first-order ODE and integrating factor
PRACTICE
P
4.
Linear first-order ODE and integrating factor
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THEORY
T
5.
Solving linear first-order ODEs
PRACTICE
P
6.
Linear first-order ODEs
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Linear second-order differential equations
THEORY
T
1.
Uniqueness of solutions of linear 2nd-order ODEs
PRACTICE
P
2.
Uniqueness of solutions of linear 2nd-order ODEs
3
THEORY
T
3.
Homogeneous linear 2nd-order ODEs with constant coefficients
PRACTICE
P
4.
Homogeneous linear 2nd-order ODEs with constant coefficients
6
THEORY
T
5.
Solving homogeneous linear ODEs with constant coefficients
PRACTICE
P
6.
Solving homogeneous linear ODEs with constant coefficients
7
THEORY
T
7.
The Ansatz
PRACTICE
P
8.
The Ansatz
5
Solution methods for linear-second order ODEs
THEORY
T
1.
The Wronskian of two differentiable functions
PRACTICE
P
2.
The Wronskian of two differentiable functions
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THEORY
T
3.
Variation of constants
PRACTICE
P
4.
Variation of constants
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THEORY
T
5.
From one to two solutions
PRACTICE
P
6.
From one to two solutions
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THEORY
T
7.
Solving linear second-order ODEs
PRACTICE
P
8.
Solving linear second-order ODEs
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Systems of differential equations
THEORY
T
1.
Systems of coupled linear first-order ODEs
PRACTICE
P
2.
Systems of coupled linear first-order ODEs
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End of Differential equations
PRACTICE
P
1.
Applications of ODEs
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THEORY
T
2.
End of Differential equations
Differential equations and Laplace transforms
Laplace-transformations
THEORY
T
1.
The Laplace transform
PRACTICE
P
2.
The Laplace transform
6
THEORY
T
3.
The inverse Laplace transform
PRACTICE
P
4.
The inverse Laplace transform
8
THEORY
T
5.
Laplace transforms of differential equations
PRACTICE
P
6.
Laplace transforms of differential equations
8
THEORY
T
7.
Convolution
PRACTICE
P
8.
Convolution
7
THEORY
T
9.
Laplace transforms of Heaviside functions
PRACTICE
P
10.
Laplace transforms of Heaviside functions
13
THEORY
T
11.
Laplace transforms of periodic functions
PRACTICE
P
12.
Laplace transforms of periodic functions
4
THEORY
T
13.
Riemann-Stieltjes integration
THEORY
T
14.
Laplace transforms of delta functions
PRACTICE
P
15.
Laplace transforms of delta functions
4
THEORY
T
16.
Transfer and response functions
PRACTICE
P
17.
Transfer and response functions
8
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